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Description

Almost Everywhere Convergence II presents the proceedings of the Second International Conference on Almost Everywhere Convergence in Probability and Ergodotic Theory, held in Evanston, Illinois on October 16–20, 1989. This book discusses the many remarkable developments in almost everywhere convergence.

Organized into 19 chapters, this compilation of papers begins with an overview of a generalization of the almost sure central limit theorem as it relates to logarithmic density. This text then discusses Hopf's ergodic theorem for particles with different velocities. Other chapters consider the notion of a log–convex set of random variables, and proved a general almost sure convergence theorem for sequences of log–convex sets. This book discusses as well the maximal inequalities and rearrangements, showing the connections between harmonic analysis and ergodic theory. The final chapter deals with the similarities of the proofs of ergodic and martingale theorems.

This book is a valuable resource for mathematicians.

Table of Contents

Contributors
Participants
Dedication
Preface
A Solution to a Problem of A. Bellow
Universal Weights from Dynamical Systems to Mean—Bounded Positive Operators on LP
Some Connections Between Ergodic Theory and Harmonic Analysis
On Hopf's Ergodic Theorem for Particles with Different Velocities
A Note on the Strong Law of Large Numbers for Partial Sums of Independent Random Vectors
Summability Methods and Almost-sure Convergence
Concerning Induced Operators and Alternating Sequences
Maximal Inequalities and Ergodic Theorems for Cesàro—α or Weighted Averages
The Hilbert Transform of the Gaussian
Mean Ergodicity of L1 Contractions and Pointwise Ergodic Theorems
Multi—Parameter Moving Averages
An Almost Sure Convergence Theorem for Sequences of Random Variables Selected from Log—Convex Sets
Divergence of Ergodic Averages and Orbital Classification of Non—singular Transformations
Some Almost Sure Convergence Properties of Weighted Sums of Martingale Difference Sequences
Pointwise Ergodic Theorems for Certain Order Preserving Mappings in L1
On the Almost Sure Central Limit Theorem
Universally Bad Sequences in Ergodic Theory
On an Inequality of Kahane
A Principle for Almost Everywhere Convergence of Multiparameter Processes

About the Editor

Alexandra Bellow

Roger L. Jones

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